Skip to main content

functions - Fixed-Point Numbers in Mathematica


I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation.


The fixed point length is 16 bit. Numbers can be represented with a variable number of bits and I can specify the format of the bits. For instance, I can represent a number as Signed[3.13], upto 3 bits are used to represent the integer portion, and 13 bits are used for the fraction (resolution of 2^-13).



Q1. What is the best method to convert Mathematica floating point output into a 16 bit number. Ideally, I’d like a function like:


f[x_, signbits_, integerbits_, fractionbits_]

Q2. Given a set of numbers, what is the best method to determine the ideal number of integer bits and fractional bits used for the representation in order to minimize truncation errors


data = {0.0000618365, 0.0000701533, -0.0000747471, 0.0000595436, 0.0000705533, \
0.0000728675, 0.0000711056, 0.0000684559, 0.0000753624, -0.0000557638}

Answer



Answering my own question from a while ago.


Turns out the easiest method is using MMA’s built-in Computer Arithmetic package


<< ComputerArithmetic`


(*Set Math Parameters*)

SetArithmetic[6, 10, ExponentRange -> {-20, 20}];

fpConvert[x_, integerbits_, fractionbits_] := ComputerNumber[IntegerPart[x] + Round[FractionalPart[x], 2^-fractionbits]];

Let’s test the output:


N[fpConvert[Pi, 3, 2], {8, 8}]
N[fpConvert[Pi, 3, 4], {8, 8}]

N[fpConvert[Pi, 3, 8], {8, 8}]
N[fpConvert[Pi, 3, 13], {8, 8}]

Works fine.


Comments

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...